Stability with respect to domain of the low Mach number limit of compressible heat-conducting viscous fluid

We investigate the asymptotic limit of solutions to the Navier-Stokes-Fourier system with the Mach number proportional to a small parameter $\varepsilon \to 0$, the Froude number proportional to $\sqrt{\varepsilon}$ and when the fluid occupies large domain with spatial obstacle of rough surface varying when $\varepsilon \to 0$. The limit velocity field is solenoidal and satisfies the incompressible Oberbeck-Boussinesq approximation. Our studies are based on weak solutions approach and in order to pass to the limit in a convective term we apply the spectral analysis of the associated wave propagator (Neumann Laplacian) governing the motion of acoustic waves

On New Examples of Families of Multivariate Stable Maps and their Cryptographical Applications

Let K be a general finite commutative ring. We refer to a familyg^n, n = 1; 2;... of bijective polynomial multivariate maps of K^n as a family with invertible decomposition gn = g^1^n g^2^n...g^k^n , such that the knowledge of the composition of g^2^nallows computation of g^2^n for O(n^s) (s > 0) elementary steps. Apolynomial map g is stable if all non-identical elements of kind g^t, t > 0 are of the same degree.We construct a new family of stable elements with invertible decomposition.This is the first construction of the family of maps based on walks on the bipartitealgebraic graphs defined over K, which are not edge transitive. We describe theapplication of the above mentioned construction for the development of streamciphers, public key algorithms and key exchange protocols. The absence of edgetransitive group essentially complicates cryptanalysis

Dynamical systems as the main instrument for the constructions of new quadratic families and their usage in cryptography

Let K be a finite commutative ring and f = f(n) a bijective polynomial map f(n) of the Cartesian power K^n onto itself of a small degree c and of a large order. Let f^y be a multiple composition of f with itself in the group of all polynomial automorphisms, of free module K^n. The discrete logarithm problem with the pseudorandom base f(n) (solvef^y = b for y) is a hard task if n is sufficiently large. We will use families of algebraic graphs defined over K and corresponding dynamical systems for the explicit constructions of such maps f(n) of a large order with c = 2 such that all nonidentical powers f^y are quadratic polynomial maps. The above mentioned result is used in the cryptographical algorithms based on the maps f(n) – in the symbolic key exchange protocols and public keys algorithms